If both the criminal and the 'innocent' parties have guns then there is a much, much higher chance of resulting causalities or deaths. Imagine a service station robbery, a criminal enters with a gun, now if the service attendant pulls out a gun, then they will both be forced to shoot (or else risk being shot), and the odds are stacked in favor of the criminal. However, if only the criminal has a gun, he merely uses it as a threat; and is not forced to use it. The same applies for house robbery's, fights, etc. Having everyone packing mac's isn't a good thing, it isn't 'safer' in any way. The criminal will always be first to draw, if the by-stander has a gun, then it is simply a greater motivation for the criminal to bust slugs to protect his neck.
You seem to be assuming that criminals are nothing more than irrational, cold hearted killing machines.
Most criminals don't want to be forced into such situations where they may be forced to kill someone and to face the very severe consequences associated with murder. Even if as you say without evidence, criminals have the upper hand, there is still a significant risk that they will end up getting shot if they attack armed citizens. Surely a high risk of being killed is a pretty strong disincentive.
Your argument only makes sense if we assume a fixed number of armed robberies, in which case more deaths may occur because firearms cause the violence to escalate. The point is that most criminals don't want to have to kill people and face the sanctions associated with murder, and they don't want to risk being killed, so an armed population creates a strong disincentive to commit a lot of property crimes in the first place.
As for those analyzing international data:
If we want to estimate the ceteris paribus effect of gun control on crime rates, it is preferable to look at how changes in gun laws effect crime rates in a given country rather than looking at different countries with different laws, demographics and socio-economic factors that influence the data. Such data exists for Australia.
Analyzing this data is still complex, some crimes have increased while others have decreased. However, what is very clear from the data is that in the 13 years since these stricter guns controls were enacted there has not been a dramatic fall in the homicide rate. In the years following the enactment of the laws homicide rates rose, since the mid 2000's they have fallen again. But the fall has not been dramatic, and is merely consistent with a long term trend of falling crime rates in Australia which was in motion before the gun laws were enacted. If as some people suggest the homicide rate in the United States is higher than Australia because of gun control (and not other differences, some of which I mentioned) we should have seen a 70% decrease in the homicide rate by now!
Protecting gun rights does not mean anyone can walk down the street with an AK-47
Gun rights are just an extension of property rights. On your own property of course you should be able to own a gun. But similarly, property owners may also say that no one may have a gun on their property. In an ancap society, public places like streets and parks would be privately owned, and regulated in this way. In today's society, most public spaces are the property of local councils, so local councils should have the right to regulate the use of guns on their property. I suspect most councils would ban the carrying of guns (unless being transported in a locked case) on the street, and I would consider this entirely appropriate and fair.
It makes sense to regulate guns at a local level, rather than a national level because different communities have different needs. For example, in Kings Cross (a Densley populated nightspot in Sydney) it would make sense for the council to ban all weapons on the streets. Protection in such a dense area can be more efficiently provided by police and private security hired by businesses in the area. You also wouldn't want drunk people carrying around guns.
On the other hand, in say, remote areas of the Northern Terrority, there is very little police can do to protect people. It could take hours to provide any sort of assistance and that's if you can even contact the police at all. I would imagine that even staunch gun control advocates would probably wish they had a gun in the car if they broke down on the side of a remote road in the NT.
If people hate guns, they should also be free to create gun free communities. For instance, a new housing estate or apartment building could require anyone who purchases a property in the development to sign a contract agreeing that they will not bring any guns onto the property, even in their own homes.